The present invention relates to wireless communication and, more particularly, wireless transmission of quaternions.
In three-dimensional space, any sequence of rotations of a coordinate system about a fixed point is mathematically equivalent to a single rotation by a given angle about a fixed axis running through the fixed point. Therefore, any rotational sequence in three dimensions can be represented as a function of a unit vector u and a rotation angle θ. Quaternions provide a simple way to express this in four numbers (a, b, c, d) computed by reference to a unit length vector having coordinates (x, y, z) relative to the x-, y- and z-axis, and a rotational angle θ, as follows:a=cos(θ/2)b=x*sin(θ/2)c=y*sin(θ/2)d=z*sin(θ/2)
Due to the ability of quaternions to describe spatial orientation and rotation of three-dimensional objects in mathematically efficient terms, quaternions have found many practical applications. For example, quaternions are used in various systems that track human movement in real-time, such as fall detection, stride monitoring, range-of-motion tracking, flexibility tracking and ergonomics monitoring. In such systems, sensor units mounted on the human body take frequent measurements (e.g., rotation, acceleration, magnetic field strength) which are converted into quaternions representing the current spatial orientation of the sensors relative to Earth. The quaternions are transmitted wirelessly to a destination computer for processing and analysis, either directly or via a wireless hub.
One shortcoming of real-time systems that transmit and consume quaternions is that known wireless communication protocols are not conducive to low latency, low power, high fidelity transmission of quaternions, especially where multiple quaternion sources transmit quaternions to a single quaternion destination over a shared wireless link. Indeed, the deficiencies in known wireless protocols with regard to quaternion transmission can render such systems prone to more frequent delays (e.g., due to transmission bottlenecks), reduced system uptime (e.g., due to sensor unit battery drain) and reduced computational accuracy (e.g., due to low data resolution).
One deficiency in known wireless protocols with regard to quaternion transmission is the absence in such protocols of predefined quaternion fields. The absence of predefined quaternion fields means extra overhead is required to specify the location and format of the quaternions being transmitted using such protocols, increasing transmission latency and system power consumption.
Furthermore, spatial orientation quaternions involve cosine and sine functions whose values vary little with angular change near +1 and −1 as compared with angular change near 0. Known wireless protocols do nothing to facilitate quaternion expression in a manner that preserves angular resolution for quaternion values near +1 or −1, which can reduce the accuracy of results computed using transmitted quaternions.